{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "from pymc3.ode import DifferentialEquation\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "import arviz as az\n",
    "import theano\n",
    "\n",
    "plt.style.use('seaborn-darkgrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GSoC 2019: Introduction of pymc3.ode API\n",
    "by [Demetri Pananos](https://dpananos.github.io/posts/2019/08/blog-post-21/)\n",
    "\n",
    "Ordinary differential equations (ODEs) are a convenient mathematical framework for modelling the temporal dynamics of a system in disciplines from engineering to ecology. Though most analyses focus on bifurcations and stability of fixed points, parameter and uncertainty estimates are more salient in systems of practical interest, such as population pharmacokinetics and pharmacodynamics.\n",
    "\n",
    "\n",
    "Both parameter estimation and uncertainty propagation are handled elegantly by the Bayesian framework.  In this notebook, I showcase how PyMC3 can be used to do inference for differential equations using the `ode` submodule.  \n",
    "\n",
    "\n",
    "# Catching Up On Differential Equations\n",
    "\n",
    "A differential equation is an equation relating an unknown function's derivative to itself.  We usually write differentual equations as \n",
    "\n",
    "$$ \\mathbf{y}' = f(\\mathbf{y},t,\\mathbf{p}) \\quad \\mathbf{y}(t_0) = \\mathbf{y}_0 $$\n",
    "\n",
    "Here, $\\mathbf{y}$ is the unknown function, $t$ is time, and $\\mathbf{p}$ is a vector of parameters.  The function $f$ can be either scalar or vector valued.\n",
    "\n",
    "Only a small subset of differential equations have an analytical solution.  For most differential equations of applied interest, numerical methods must be used to obtain approximate solutions.\n",
    "\n",
    "\n",
    "# Doing Bayesian Inference With Differential Equations\n",
    "\n",
    "PyMC3 uses Hamiltonian Monte Carlo (HMC) to obtain samples from the posterior distribution.  HMC requires derivatives of the ODE's solution with respect to the parameters $p$.  The `ode` submodual automatically computes appropriate derivatives so you don't have to.  All you have to do is \n",
    "\n",
    "* Write the differential equation as a python function\n",
    "* Write the model in PyMC3\n",
    "* Hit the Inference Button $^{\\text{TM}}$\n",
    "\n",
    "Let's see how this is done in practice with a small example.\n",
    "\n",
    "# A Differential Equation For Freefall\n",
    "\n",
    "An object of mass $m$ is brought to some height and allowed to fall freely until it reaches the ground. A differential equation describing the object's speed over time is \n",
    "\n",
    "$$ y' = mg - \\gamma y $$\n",
    "\n",
    "The force the object experiences in the downwards direction is $mg$, while the force the object experiences in the opposite direction (due to air resistance) is proportional to how fast the object is presently moving. Let's assume the object starts from rest (that is, that the object's inital velocity is 0).  This may or may not be the case.  To showcase how to do inference on intial conditions, I will first assume the object starts from rest, and then relax that assumption later.\n",
    "\n",
    "Data on this object's speed as a function of time is shown below.  The data may be noisy because of our measurement tools, or because the object is an irregular shape, thus leading to times during freefall when the object is more/less aerodynamic.  Let's use this data to estimate the proportionality constant for air resistance.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For reproducibility\n",
    "np.random.seed(20394)\n",
    "\n",
    "def freefall(y, t, p):    \n",
    "    return 2.0*p[1] - p[0]*y[0]\n",
    "\n",
    "# Times for observation\n",
    "times = np.arange(0,10,0.5)\n",
    "gamma,g, y0, sigma = 0.4, 9.8, -2, 2\n",
    "y = odeint(freefall, t=times, y0=y0, args=tuple([[gamma,g]]))\n",
    "yobs = np.random.normal(y,2)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=120)\n",
    "plt.plot(times,yobs, label='observed speed', linestyle='dashed', marker='o', color='red')\n",
    "plt.plot(times,y, label='True speed', color='k', alpha=0.5)\n",
    "plt.legend()\n",
    "plt.xlabel('Time (Seconds)')\n",
    "plt.ylabel(r'$y(t)$');\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To specify and ordinary differential equation with pyMC3, use the `DifferentialEquation` class.  This class takes as arguments:\n",
    "\n",
    "* `func`: A function specifying the differential equation (i.e. $f(\\mathbf{y},t,\\mathbf{p})$).\n",
    "* `times`: An array of times at which data was observed.\n",
    "* `n_states`: The dimension of $f(\\mathbf{y},t,\\mathbf{p})$.\n",
    "* `n_theta`: The dimension of $\\mathbf{p}$.\n",
    "* `t0`: Optional time to which the initial condition belongs.\n",
    "\n",
    "The argument `func` needs to be written as if `y` and `p` are vectors.  So even when your model has one state and/or one parameter, you should explicitly write `y[0]` and/or `p[0]`.\n",
    "\n",
    "Once the model is specified, we can use it in our pyMC3 model by passing parameters and inital conditions.  `DifferentialEquation` returns a flattened solution, so you will need to reshape it to the same shape as your observed data in the model.\n",
    "\n",
    "Shown below is a model to estimate $\\gamma$ in the ODE above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [gamma, sigma]\n",
      "Sampling chain 0, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [02:08<00:00, 23.28it/s]\n",
      "Sampling chain 1, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [01:57<00:00, 25.63it/s]\n",
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4000/4000 [00:42<00:00, 93.03it/s]\n"
     ]
    }
   ],
   "source": [
    "ode_model = DifferentialEquation(\n",
    "    func=freefall,\n",
    "    times=times,\n",
    "    n_states=1, n_theta=2,\n",
    "    t0=0\n",
    ")\n",
    "\n",
    "with pm.Model() as model:\n",
    "    # Specify prior distributions for soem of our model parameters\n",
    "    sigma = pm.HalfCauchy('sigma',1)    \n",
    "    gamma = pm.Lognormal('gamma',0,1)\n",
    "    \n",
    "    # If we know one of the parameter values, we can simply pass the value.\n",
    "    ode_solution = ode_model(y0=[0], theta=[gamma, 9.8])\n",
    "    # The ode_solution has a shape of (n_times, n_states)\n",
    "    \n",
    "    Y = pm.Normal('Y', mu=ode_solution, sd=sigma, observed=yobs)\n",
    "    \n",
    "    prior = pm.sample_prior_predictive()\n",
    "    trace = pm.sample(2000, tune=1000, cores=1)\n",
    "    posterior_predictive = pm.sample_posterior_predictive(trace)\n",
    "    \n",
    "    data = az.from_pymc3(trace=trace, prior=prior, posterior_predictive=posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our estimates of the proportionality constant and noise in the system are incredibly close to their actual values!\n",
    "\n",
    "We can even estimate the acceleration due to gravity by specifying a prior for it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [g, gamma, sigma]\n",
      "Sampling chain 0, 0 divergences:   0%|                                                                                                                                               | 0/3000 [00:00<?, ?it/s]C:\\Users\\osthege\\AppData\\Local\\Continuum\\miniconda3\\envs\\pm3-dev\\lib\\site-packages\\scipy\\integrate\\odepack.py:247: ODEintWarning: Illegal input detected (internal error). Run with full_output = 1 to get quantitative information.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n",
      "Sampling chain 0, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [07:41<00:00,  6.50it/s]\n",
      "Sampling chain 1, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [08:03<00:00,  6.21it/s]\n",
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4000/4000 [00:41<00:00, 96.80it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model2:    \n",
    "    sigma = pm.HalfCauchy('sigma',1)\n",
    "    gamma = pm.Lognormal('gamma',0,1)\n",
    "    # A prior on the acceleration due to gravity\n",
    "    g = pm.Lognormal('g',pm.math.log(10),2)\n",
    "    \n",
    "    # Notice now I have passed g to the odeparams argument\n",
    "    ode_solution = ode_model(y0=[0], theta=[gamma, g])\n",
    "    \n",
    "    Y = pm.Normal('Y', mu=ode_solution, sd=sigma, observed=yobs)\n",
    "\n",
    "    prior = pm.sample_prior_predictive()\n",
    "    trace = pm.sample(2000, tune=1000, target_accept=0.9, cores=1)\n",
    "    posterior_predictive = pm.sample_posterior_predictive(trace)\n",
    "    \n",
    "    data = az.from_pymc3(trace=trace, prior=prior, posterior_predictive=posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1490.4x331.2 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainty in the acceleration due to gravity has increased our uncertainty in the proportionality constant.\n",
    "\n",
    "Finally, we can do inference on the initial condition.  If this object was brought to its initial height by an airplane, then turbulent air might have made the airplane move up or down, thereby changing the inital velocity of the object. \n",
    "\n",
    "Doing inference on the initial condition is as easy as specifying a prior for the inital condition, and then passing the inital condition to `ode_model`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [y0, g, gamma, sigma]\n",
      "Sampling chain 0, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [11:00<00:00,  4.54it/s]\n",
      "Sampling chain 1, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [09:51<00:00,  5.07it/s]\n",
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4000/4000 [00:41<00:00, 96.92it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model3:    \n",
    "    sigma = pm.HalfCauchy('sigma',1)\n",
    "    gamma = pm.Lognormal('gamma',0,1)\n",
    "    g = pm.Lognormal('g',pm.math.log(10),2)\n",
    "    # Initial condition prior.  We think it is at rest, but will allow for perturbations in initial velocity.\n",
    "    y0 = pm.Normal('y0', 0, 2)\n",
    "    \n",
    "    ode_solution = ode_model(y0=[y0], theta=[gamma, g])\n",
    "    \n",
    "    Y = pm.Normal('Y', mu=ode_solution, sd=sigma, observed=yobs)\n",
    "    \n",
    "    prior = pm.sample_prior_predictive()\n",
    "    trace = pm.sample(2000, tune=1000, target_accept=0.9, cores=1)\n",
    "    posterior_predictive = pm.sample_posterior_predictive(trace)\n",
    "    \n",
    "    data = az.from_pymc3(trace=trace, prior=prior, posterior_predictive=posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(data, figsize=(13,3));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that by explicitly modelling the initial condition, we obtain a much better estimate of the acceleration due to gravity than if we had insisted that the object started at rest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-linear Differential Equations\n",
    "\n",
    "The example of an object in free fall might not be the most appropriate since that differential equation can be solved exactly. Thus, `DifferentialEquation` is not needed to solve that particular problem.  There are, however, many examples of differential equations which cannot be solved exactly.  Inference for these models is where `DifferentialEquation` truly shines.\n",
    "\n",
    "Consider the SIR model of infection.  This model describes the temporal dynamics of a disease spreading through a homogenously mixed closed population.  Members of the population are placed into one of three cateories: Susceptible, Infective, or Recovered.  The differential equations are...\n",
    "\n",
    "\n",
    "$$ \\dfrac{dS}{dt} = - \\beta SI \\quad S(0) = S_0 $$\n",
    "$$ \\dfrac{dI}{dt} = \\beta SI - \\lambda I \\quad I(0) = I_0 $$\n",
    "$$ \\dfrac{dR}{dt} = \\lambda I \\quad R(0) = R_0 $$\n",
    "\n",
    "With the constraint that $S(t) + I(t) + R(t) = 1 \\, \\forall t$. Here, $\\beta$ is the  rate  of infection per susceptible and per infective, and $\\lambda$ is the rate of recovery.\n",
    "\n",
    "If we knew $S(t)$ and $I(t)$, then we could determine $R(t)$, so we can peel off the differential equation for $R(t)$ and work only with the first two.  \n",
    "\n",
    "\n",
    "In the SIR model, it is straight-forward to see that $\\beta, \\gamma$ and $\\beta/2, \\gamma/2$ will produce the same qualitative dynamics but on much different time scales.  To study the *quality* of the dynamics, regardless of time scale, applied mathematicians will *non-dimensionalize* differential equations.  Non-dimensionalization is the process of introducing scaleless variables into the differential equation to understand the system's dynamics under families of equivalent paramterizations.\n",
    "\n",
    "To non-dimensionalize this system, let's scale time by $1/\\lambda$ (we do this because people stay infected for an average of $1/\\lambda$ units of time.  It is a straight forward argument to show this.  For more, see [1]).  Let $t = \\tau/\\lambda$, where $\\tau$ is a unitless variable.  Then...\n",
    "\n",
    "\n",
    "$$ \\dfrac{dS}{d\\tau} = \\dfrac{dt}{d\\tau} \\dfrac{dS}{dt} = \\dfrac{1}{\\lambda}\\dfrac{dS}{dt} = -\\dfrac{\\beta}{\\lambda}SI$$\n",
    "\n",
    "and \n",
    "\n",
    "$$ \\dfrac{dI}{d\\tau} = \\dfrac{dt}{d\\tau} \\dfrac{dI}{dt} = \\dfrac{1}{\\lambda}\\dfrac{dI}{dt} = \\dfrac{\\beta}{\\lambda}SI - I$$\n",
    "\n",
    "The quantity $\\beta/\\lambda$ has a very special name.  We call it *The R-Nought* ($\\mathcal{R}_0$).  It's interpretation is that if we were to drop a single infected person into a population of suceptible individuals, we would expect $\\mathcal{R}_0$ new infections.  If $\\mathcal{R}_0>1$, then an epidemic will take place.  If $\\mathcal{R}_0\\leq1$ then there will be no epidemic (note, we can show this more rigoursly by studying eigenvalues of the system's Jacobain.  For more, see [2]).\n",
    "\n",
    "This non-dimensionalization is important because it gives us information about the parameters.  If we see an epidemic has occured, then we know that $\\mathcal{R}_0>1$ which means $\\beta> \\lambda$. Furthermore, it might be hard to place a prior on $\\beta$ because of beta's interpretation.  But since $1/\\lambda$ has a simple interpretation, and since $\\mathcal{R}_0>1$, we can obtain $\\beta$ by computing $\\mathcal{R}_0\\lambda$. \n",
    "\n",
    "Side note: I'm going to choose a likelihood which certainly violates these constraints, just for exposition on how to use `DifferentialEquation`.  In reality, a likelihood which respects these constraints should be chosen.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def SIR(y, t, p):\n",
    "    ds = -p[0]*y[0]*y[1]\n",
    "    di = p[0]*y[0]*y[1] - p[1]*y[1]    \n",
    "    return [ds, di]\n",
    "\n",
    "times = np.arange(0,5,0.25)\n",
    "\n",
    "beta,gamma = 4,1.0\n",
    "# Create true curves\n",
    "y = odeint(SIR, t=times, y0=[0.99, 0.01], args=((beta,gamma),), rtol=1e-8)\n",
    "# Observational model.  Lognormal likelihood isn't appropriate, but we'll do it anyway\n",
    "yobs = np.random.lognormal(mean=np.log(y[1::]), sigma=[0.2, 0.3])\n",
    "\n",
    "\n",
    "plt.plot(times[1::],yobs, marker='o', linestyle='none')\n",
    "plt.plot(times, y[:,0], color='C0', alpha=0.5, label=f'$S(t)$')\n",
    "plt.plot(times, y[:,1], color ='C1', alpha=0.5, label=f'$I(t)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Sequential sampling (2 chains in 1 job)\n",
      "NUTS: [lambda, R0, sigma]\n",
      "Sampling chain 0, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [20:55<00:00,  2.39it/s]\n",
      "Sampling chain 1, 0 divergences: 100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 3000/3000 [20:11<00:00,  2.48it/s]\n",
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4000/4000 [02:19<00:00, 28.66it/s]\n"
     ]
    }
   ],
   "source": [
    "sir_model = DifferentialEquation(\n",
    "    func=SIR, \n",
    "    times=np.arange(0.25, 5, 0.25), \n",
    "    n_states=2,\n",
    "    n_theta=2,\n",
    "    t0=0,\n",
    ")\n",
    "\n",
    "with pm.Model() as model4:    \n",
    "    sigma = pm.HalfCauchy('sigma', 1, shape=2)\n",
    "    \n",
    "    # R0 is bounded below by 1 because we see an epidemic has occured\n",
    "    R0 = pm.Bound(pm.Normal, lower=1)('R0', 2,3)\n",
    "    lam = pm.Lognormal('lambda',pm.math.log(2),2)\n",
    "    beta = pm.Deterministic('beta', lam*R0)\n",
    "    \n",
    "    sir_curves = sir_model(y0=[0.99, 0.01], theta=[beta, lam])\n",
    "    \n",
    "    Y = pm.Lognormal('Y', mu=pm.math.log(sir_curves), sd=sigma, observed=yobs)\n",
    "\n",
    "    prior = pm.sample_prior_predictive()\n",
    "    trace = pm.sample(2000,tune=1000, target_accept=0.9, cores=1)\n",
    "    posterior_predictive = pm.sample_posterior_predictive(trace)\n",
    "    \n",
    "    data = az.from_pymc3(trace=trace, prior = prior, posterior_predictive = posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1490.4x662.4 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(data,round_to=2, credible_interval=0.95);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from the posterior plots, $\\beta$ is well estimated by leveraging knoweldege about the non-dimensional parameter $\\mathcal{R}_0$ and $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions & Final Thoughts\n",
    "\n",
    "ODEs are a really good model for continuous temporal evolution.  With the addition of `DifferentialEquation` to PyMC3, we can now use bayesian methods to estimate the parameters of ODEs.\n",
    "\n",
    "`DifferentialEquation` is not as fast as compared to Stan's `integrate_ode_bdf`.  However, the ease of use of `DifferentialEquation` will allow practioners to get up and running much quicker with Bayesian estimation for ODEs than Stan (which has a steep learning curve).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "1. Earn, D. J., et al. Mathematical epidemiology. Berlin: Springer, 2008.\n",
    "2. Britton, Nicholas F. Essential mathematical biology. Springer Science & Business Media, 2012.\n"
   ]
  }
 ],
 "metadata": {
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   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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